A process for treating a semiconductor wafer (e.g., a silicon wafer) used for a semiconductor includes controlling an in-plane temperature distribution of the semiconductor wafer as desired while controlling a temperature of the semiconductor wafer to a temperature setpoint.
Accordingly, the temperature of the semiconductor wafer is typically controlled to a desired temperature by providing a plurality of temperature adjusters and control loops to the respective temperature adjusters and independently controlling the temperature adjusters with the control loops. As one of such multi-input multi-output control methods, a model following servo control method is used.
The model following servo control method includes: selecting a model (e.g., a second-order lag system) having dynamic characteristics generally desired as a reference model; and providing a setpoint response to make a control variable to follow a step response of the reference model as a reference trajectory.
In order to improve a throughput in the process, it is desirable to intentionally saturate the manipulated variable to reach a setpoint at the maximum speed in the shortest time.
Patent Literature 1 (JP2016-12228A) discloses a technology of generating a reference model based on a response in which, in a plurality of control loops, a manipulated variable of a first control loop having the slowest response speed is defined as 100% and the rest of the control loops is controlled to follow the first control loop; with use of the generated reference model, searching for a manipulated variable pattern, using a predetermined evaluation function, for reaching the temperature setpoint in the shortest time; giving a manipulated variable of the searched optimal manipulated variable pattern to the reference model to obtain an output; and using the obtained output as a reference model output.
However, since the technology of Patent Literature 1 includes searching for a switching time allowable for the minimum evaluation function, in other words, a switching time allowable for a small overshoot and a short setting time, the obtained results do not always completely conform with a setpoint, which entails a problem that there is a possibility to cause an error with respect to the setpoint.